<div><p>Honeycomb layered oxides are a novel class of materials generally exhibiting high ionic conductivity with battery applications. Owing to their honeycomb structure and layered framework, this class of materials is thought to harbor unique electrochemistry and physics. Here, a heuristic diffusion model of the charged alkali cations (such as lithium, sodium or potassium) in two-dimensional (2D) honeycomb layers within the three-dimensional (3D) crystal of honeycomb layered oxide is

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... . The model relates the excitation of cationic vacancies (by applied electromagnetic fields) to the Gaussian curvature deformation of the 2D surface. The quantum properties of the cations and their interlayer mixing through quantum tunneling are also considered. This work offers a novel theoretical framework for the study of 3D layered materials with 2D cationic diffusion currents, whilst providing pedagogical insights in the role of geometry in Brownian motion and quantum theory.</p><br></div>